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On a Two-dimensional Elliptic Problem with Large Exponent in Nonlinearity
| Content Provider | Semantic Scholar |
|---|---|
| Author | Abstract, Juncheng W. E. I. |
| Copyright Year | 1994 |
| Abstract | A semilinear elliptic equation on a bounded domain in R2 with large exponent in the nonlinear term is studied in this paper. We investigate positive solutions obtained by the variational method. It turns put that the constrained minimizing problem possesses nice asymptotic behavior as the nonlinear exponent, serving as a parameter, gets large. We shall prove that cp , the minimum of energy functional with the nonlinear exponent equal to p , is like (&Ke)lf2p~^2 as p tends to infinity. Using this result, we shall prove that the variational solutions remain bounded uniformly in p . As p tends to infinity, the solutions develop one or two peaks. Precisely the solutions approach zero except at one or two points where they stay away from zero and bounded from above. Then we consider the problem on a special class of domains. It turns out that the solutions then develop only one peak. For these domains, the solutions enlarged by a suitable quantity behave like a Green's function of -A. In this case we shall also prove that the peaks must appear at a critical point of the Robin function of the domain. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.ubc.ca/~jcwei/ren-TAMS1994.pdf |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1994-343-02/S0002-9947-1994-1232190-7/S0002-9947-1994-1232190-7.pdf |
| Alternate Webpage(s) | http://www.ima.umn.edu/~ren/ps/bddr2.ps |
| Alternate Webpage(s) | http://home.gwu.edu/~ren/pub/bddr2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Calculus of variations Cerebral Palsy Commutation theorem Critical point (network science) Enlargement procedure Exponent Infinity Nonlinear system Population Parameter Solutions |
| Content Type | Text |
| Resource Type | Article |
